A near-quadratic algorithm for planning the motion of a polygon in a polygonal environment

We consider the problem of planning the motion of an arbitraryk-sided polygonal robotB, free to translate and rotate in a polygonal environmentV bounded byn edges. We present an algorithm that constructs a single component of the free configuration space ofB in timeO((kn)2+ɛ), for any ɛ>0. This algorithm, combined with some standard techniques in motion planning, yields a solution to the underlying motion-planning problem, within the same running time.

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